Typically, an axial gap is provided between a high pressure turbine shroud and the outer wall of a downstream gas path duct at ambient temperatures, to allow for thermal expansion of the duct and/or the turbine shroud at engine operating temperatures. The magnitude of such thermal expansion can be predicted, and the gap sized, so that thermal expansion generally seals the gap to prevent leakage through the gap. However, the seal is not perfect and it must be ensured to adequately purge the adjacent cavity with sufficient cooling air to avoid hot gas ingestion. Reducing such uses of secondary air can increase gas turbine engine efficiency, however, and accordingly there is room for improvement.